Bingo

February 19, 2009

Bingo is a children’s game of chance, sometimes played by adults for fun or money. Each player has a card of numbers arranged in a five-by-five grid with five randomly-chosen numbers from 1 to 15 in the first column, from 16 to 30 in the second column, 31 to 45 in the third column, 46 to 60 in the fourth column, and 61 to 75 in the fifth column; the central space is “free” and is considered to be occupied. Then a caller randomly calls numbers from 1 to 75 without replacement, each player marking the corresponding number, if it is present on their card, as occupied. The first player to have five occupied numbers in a row horizontally, in a column vertically, or along either of the two major diagonals is the winner.

What is the average number of calls required before a single card achieves bingo? In a large game with five hundred cards in play, what is the average number of calls required before any card achieves bingo?

Here is my single card bingo simulation.
Checkout the implementation of 500 cards at given link: http://codepad.org/yjsI6jiz
As expected, the average number of calls for 500 cards is coming out much less then single card